Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23782145 | C2 | semidirect |
| 3. #23781778 | C2 | semidirect |
| 4. #23781773 | C2 | semidirect |
| 5. C4×#14579688 | C2 | semidirect |
| 6. C2×#19104667 | C2 | semidirect |
| 7. #23781667 | C2 | semidirect |
| 8. #405×C163 | C2 | semidirect |
| 10. #19104757 | C4 | semidirect |
| 30. #14579699 | C2×C4 | semidirect |
| 37. Dic652 | C2×C4 | semidirect |
| 38. #14579688 | C2×C4 | semidirect |
| 39. D1304 | C2×C4 | semidirect |
| 47. C2×C8×C163 | C2×C4 | semidirect |
| 90. C163 | #2952 | semidirect |
| 99. #405 | D163 | semidirect |
| 133. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| #23782145 | 2 |
| #23781778 | 2 |
| #23781773 | 2 |
| C4×#14579688 | 2 |
| C2×#19104667 | 2 |
| #23781667 | 2 |
| #405×C163 | 2 |
| #2952 | 163 |